Compressible flow: Turbulence at the surface

In a study of compressible flow, we have tracked the motion of particles that float on a turbulent body of water. The second moment of longitudinal velocity differences scales as in incompressible flow. However the separation OR2(t)P of particle pairs does not vary in time according to the Richardson–Kolmogorov prediction OR2(t)P3 t3. As expected, the self diffusion Od2(t)P shows a cross-over between ballistic motion Od2(t)P3 t2 at small t and uncorrelated motion Od2(t)P3 t in the longtime limit